Quote by Mentz114
Yes, the length of a vector changing on transport around a loop is hard to imagine.
Where's the best place to read about this theory ?

I liked Eddington's description  see #3. The book is public domain and available online at that link.
Quote by Mentz114
There are probably mathematical reasons why a scalar deficit can't work as a repository of gravity.

In the Weyl theory it's used as a geometric description of the electromagnetic field, not gravity.